CLARIFICATION OF THE SLOPE MASS RATING PARAMETERS …

This is a preprint version of the article published by Springer in Bulletin of Engineering Geology and the Environment. This paper has to be cited as: Pastor, J.L., Riquelme, A.J., Tomás, R. et al. Clarification of the slope mass rating parameters assisted by SMRTool, an open-source software. Bull Eng Geol Environ 78, 6131–6142 (2019). https://doi.org/10.1007/s10064-019-01528-9

1

CLARIFICATION OF THE SLOPE MASS RATING 1

PARAMETERS ASSISTED BY SMRTOOL, AN OPEN-SOURCE 2

SOFTWARE 3

José Luis Pastor*, Adrián J. Riquelme, Roberto Tomás, Miguel Cano 4

Department of Civil Engineering. University of Alicante, P.O. Box 99, 03080, 5

Alicante, Spain. 6

* Corresponding author. [email protected] Tel.: +34 965903400 Ext 2470; fax: +34 7

965903678 8

ABSTRACT 9

Geomechanics classifications are used to perform a preliminary assessment of rock slopes 10

stability for different purposes in civil and mining engineering. Among all existing rock mass 11

classifications, Slope Mass Rating (SMR) is one of the most commonly used for slopes. Although 12

SMR is a worldwide applied geomechanics classification, often some misapprehensions and 13

inaccuracies are made when professionally and scientifically used. Nearly all these miscalculations 14

involve the influence of slope geometry and the dip and direction of the discontinuities. These 15

problems can be overcome by a systematic assessment of SMR, which allow users to understand and 16

visualize the relative orientation between discontinuities and slope. To fulfil this purpose a complete 17

and detailed definition of the angular relationships between discontinuities and slope are included in 18

this paper, clarifying the assessment of the SMR parameters. Additionally, a Matlab-based open-19

source software for Slope Mass Rating (SMRTool) calculation is presented, avoiding miscalculations 20

by automating the calculations and showing the graphical representation of slope and discontinuities. 21

Finally, a general explanation of the method for the use of SMR is reviewed, stressing at the common 22

source of errors when applying this classification. The performance, benefits and usefulness of 23

SMRTool are also illustrated in this paper throughout a specific case study. 24

Keywords: geology; rock mechanics; Matlab; Slope Mass Rating (SMR); geomechanical 25

classification. 26

27

1. INTRODUCTION 28

Geomechanics classifications are used to perform a preliminary assessment of rock 29

slopes stability for different purposes in civil and mining engineering. These classifications, 30

based on an empirical approach, are of paramount importance at the first stages of a project 31

due to its simplicity, enabling a preliminary assessment of the stability of many slopes in a 32

relatively short period of time. Some of the existing geomechanics classifications for slopes 33

This is a preprint version of the article published by Springer in the Bulletin of Engineering Geology and the Environment, 2019. https://doi.org/10.1007/s10064-019-01528-9

2

are Rock Mass Rating (RMR) (Bieniawski 1976, 1989), Slope Mass Rating (SMR) (Romana 34

1993), Rock Mass Strength (RMS) (Romana 1985), Slope Rock Mass Rating (SRMR) 35

(Robertson 1988), Slope Stability Probability Classification (SSPC) (Hack et al. 1998), 36

Modified Stability Probability Classification (SSPC modified) (Lindsay et al. 2001), Natural 37

Slope Methodology (NSM) (Shuk 1994) and Q-slope Method (Barton and Bar 2015; Bar and 38

Barton 2017). Among all, Slope Mass Rating (SMR), calculated on the base of Rock Mass 39

Rating (RMR), is probably one of the most widely used classifications (Romana et al. 2015). 40

Many technical and educational books of rock mechanics or rock slope stability include a 41

specific chapter or section for this classification (e.g. Hudson and Harrison (1997); Singh and 42

Göel (1999)). SMR has also been included in technical regulations of some countries such as 43

Italy, USA, China and India (Romana et al. 2015; Tomás et al. 2016). 44

The assessment of the basic RMR is made by rating five parameters: 1) rock strength, 45

2) rock quality, 3) spacing, 4) condition of discontinuities, and 5) groundwater conditions. 46

Once the basic RMR has been calculated, four new factors have to be taken into account to 47

calculate the SMR index. These new factors depend on the method of excavation of the slope 48

and the relative orientation between discontinuities and slope. SMR value varies between 0 49

and 100, being 0 a completely unstable slope and 100 a completely stable one. It is important 50

to note that other values are mathematically possible, although those values higher than 100 or 51

lower than 0 do not have a physical sense. 52

Despite the apparent simplicity of this classification, often some mistakes are made 53

when it is used for professional and scientific purposes. Nearly all these mistakes involve the 54

influence of slope geometry and the strike and dip of the discontinuities. As a consequence of 55

these mistakes, the final result of the slope stability assessment can be completely inaccurate. 56

In this sense, Zheng et al. (2016) observed some problems assessing the two adjustment 57

parameter F1 and F3, considering that the original SMR system may contain theory defects. 58

But actually, it is a clarification of the SMR parameters what is needed. This clarification is 59

presented in this paper through a comprehensive review of the SMR index (section 2). In 60

section 3, a complete and detailed definition of the angular relationships between 61

discontinuities and slope, and a redefinition of the mathematical equations for all the possible 62

cases are included. Additionally, to avoid potential misunderstandings, a new Matlab-based 63

open-source software has been developed in order to overcome the difficulties in the SMR 64

calculation (section 4). The performance, benefits and usefulness of SMRTool are also 65


3

illustrated and discussed in this paper throughout a specific case study in section 5. Finally, 66

the main conclusions are presented in section 6. 67

68

2. SLOPE MASS RATING 69

Rock Mass Rating (RMR) system was originally published by Bieniawski in 1976 70

(Bieniawski 1976). Since then, the RMR classification system has experienced successively 71

changes in the ratings assigned to different parameters as more case reports were studied 72

(Bieniawski 1989). Five parameters are used to classify a rock mass using the RMR 73

classification: uniaxial compressive strength of rock, Rock Quality Designation (RQD), 74

spacing of discontinuities, condition of discontinuities (further subdivided into persistence, 75

separation, smoothness, infilling and weathering) and groundwater conditions. The value of 76

RMR is equal to the sum of all these five parameters and it ranges from 0 to 100. 77

SMR index is obtained from basic RMR according to equation (1), taking into account 78

four new parameters (F1, F2, F3 and F4) that consider the probability of failure of the slope 79

depending on the slope method of excavation and the relative orientation between the 80

discontinuities and the slope. It is worth noting that the parameters F1, F2 and F3 depend on 81

the expected type of failure for the slope under consideration (Fig. 1 ). 82

83

(1) 84

85

where 86

F1 depends on the angle A ( Fig. 2 toFig. 4 and Table 1) between the 87

discontinuity dip direction and slope dip direction (i.e. the parallelism between: a) 88

the strikes of the discontinuity and the slope for planar and toppling failures; and b) 89

the azimuth of the line of intersection and the dip direction of the slope for wedge 90

failure). 91

F2 depends on the discontinuity dip angle (B) (Fig. 2 to Fig. 4 and Table 1 92

F3 depends on (Fig. 2 to Fig. 4 and Table 1): a) the difference (C) between the 93

discontinuity and the slope dip angles for plane failure; b) the sum (C) of the 94

discontinuity and the slope dip angles for toppling; or c) the difference (C) between 95

the plunge of the line of intersection and the slope dip angle for wedge failure. 96

F4 depends on the excavation method (Table 1). 97


4

98

Fig. 1 – Types of possible slope failure to be considered in SMR calculation (Hoek and Bray 99

1981). 100

101

102

Fig. 2 – Parallelism (A) between discontinuity ( ) and slope ( ) strikes for planar failure. 103


5

104

Fig. 3 – Parallelism (A) between discontinuity ( ) and slope ( ) strikes for toppling failure. 105

106

107

Fig. 4 – Parallelism (A) between the plunge direction of the line of intersection of two 108

discontinuities ( ) and the slope dip direction ( ). 109

110


6

The rating of these four parameters for the SMR calculation is shown in Table 1, in 111

which it can be seen that orientation-dependent factors are zero or negative, while the 112

excavation method factor can be positive or negative. 113

114

Table 1. Adjusting factors for discontinuities (F1, F2, and F3) and excavation method 115

(F4). Modified from Romana (1985) by Tomás et al. (2007). 116

Auxiliary angle

Adjusting factor

Very

favourable Favourable Fair Unfavourable

Very

unfavourable

A > 30º 30º - 20º 20º - 10º 10º - 5º < 5º

F1 0.15 0.40 0.70 0.85 1.00

B < 20º 20º - 30º 30º - 35º 35º - 45º > 45º

F2 0.15 0.40 0.70 0.85 1.00

1.00

C > 10º 10º - 0º 0º 0º - (-10º) < (-10º)

< 110º 110 - 120º > 120º - -

F3 0 -6 -25 -50 -60

Excavation

method Natural slope Presplitting

Smooth

blasting

Blasting or

mechanical

Deficient

blasting

F4 +15 +10 +8 0 -8

117

In order to make computation simpler, Romana (1993) proposed the following 118

continuous function for F1 and F2 as alternative values to that shown in Table 1: 119

120

F1 = (1 – sen |A|)2 (2) 121

F2 = tan2 B (3) 122

123

In order to reduce subjective interpretations in the assignation of the values near the 124

borders of the intervals, Tomás et al. (2007) proposed asymptotical continuous functions for 125

F1, F2 and F3 correction factors (Table 2) that show maximum absolute differences with 126

discrete functions lower than 7 points. These functions can be also easily implemented into 127

software routines for SMR assessment. 128

129

130

131

132


7

Table 2. Asymptotical continuous functions for F1, F2 and F3 calculation, (Tomás et al. 133

2007). 134

Parameter Planar failure Toppling failure

F1

F2

F3

A is equal to the parallelism between discontinuities and slope strikes for planar and toppling failures and the angle formed

between the intersection of the two discontinuities (the plunge direction) and the slope dip direction for wedge failure.

B = βj or βi

C = βj - βs for plane failure, C = βi - βs for wedge failure and C = βj + βs for toppling failure.

βj = joint dip angle; βi = line of joint intersection dip angle; βs = slope dip angle.

Note that atan has to be expressed in degrees.

135

Once the SMR of a slope has been calculated, the slope can be classified within one of 136

the five different stability classes shown in Table 3. Each one of these classes is associated 137

empirically with a different failure mode. Table 3 also provides recommendations of remedial 138

measurements of a slope based on SMR depending on the stability class. 139

140

Table 3. Description of SMR classes (Romana 1985). 141

Class nº V IV III II I

SMR 0 - 20 21 - 40 41 - 60 61 - 80 81 - 100

Description Very bad Bad Fair Good Very good

Stability Completely unstable Unstable Partially stable Stable Completely unstable

Failures Big planar or soil-like Planar or big wedges Some joints or

many wedges Some blocks None

Support Reexcavation Important / corrective Systematic Occasional none

142

3. DETAILED DESCRIPTION OF SMR CORRECTION FACTORS 143

The correct and accurate determination of parameters F1, F2 and F3 is crucial for a 144

reliable calculation of the SMR index. SMR is especially sensitive to F1 and F2 parameters 145

(Tomás et al. 2012b), since their product (=F1F2) can be considered as the percentage of 146

factor F3 mobilized (Tomás et al. 2012a). Therefore, a special attention has to be paid in the 147

calculation of the auxiliary angular relationships. A wrong determination of some of the 148


8

correction parameters can lead to a sub-estimation or an overestimation of the geomechanic 149

quality of the slope and, thus, of the evaluation of its stability. 150

The first step for a systematic definition of the parameters is the description of the involved 151

variables. To this aim, hereinafter, it is adopted that αj and αs are the discontinuity and slope 152

dip directions and βj and βs the discontinuity and slope dip angles, respectively. Three 153

auxiliary angles are used to define F1, F2 and F3 adjustment factors: A, B and C, as defined by 154

Tomás et al. (2007). 155

A refers to the parallelism between discontinuities and slope strike for planar and 156

toppling failures (Fig. 2 and Fig. 3) and the angle formed between the intersection of the two 157

discontinuities (the plunge direction) and the slope dip direction for wedge failure (Fig. 4 ). 158

Originally, Romana (1985) stated in a general way that the parallelism (i.e. A angle) could be 159

calculated as: 160

(4) 161

162

However, these formulas are not valid for the calculus of the parallelism between the slope 163

and the discontinuity (A) in all possible relative orientations, leading to errors in its 164

calculation and therefore in the estimation of SMR. According to (4), angles higher than 90º 165

are possible, although the parallelism between the discontinuity and slope strikes has to be 166

always equal or less than 90º. This is the main source of error when calculating SMR and 167

thus, a detailed description of this parameter is required as follows. When |αj - αs| is less than 168

90º planar failure is expected and A is directly equal |αj - αs|. Nevertheless, a mathematical 169

correction is needed in all other cases. When |αj - αs| is higher than 270º planar failure is also 170

expected but A is equal to 360º - |αj - αs|. Toppling failure is expected when |αj - αs| is between 171

90º and 270º, so in this case, instead of the equation |αj - αs - 180º| which is only valid when αj 172

≥ αs, the most general equation ||αj - αs| - 180º| should be used to the assessment of A. For 173

wedge failure, the two joints intersection line dip direction (αi) is taken into account to study 174

the parallelism between this line and the slope dip direction. When |αi - αs| is less than 90º or 175

higher than 270º a wedge failure can happen. Nevertheless, when |αi - αs| is between 90º and 176

270º the wedge failure is kinematically not feasible (i.e. the wedge dips towards the slope), 177

Fig. 5. 178


9

179

Fig. 5 – Calculation of the auxiliary angle A for a) planar and toppling failure and b) Wedge 180

failure. The figure can be turned to make αs perpendicular to the strike of the slope under 181

consideration. 182

B angle is less problematic when calculated. The auxiliary angle B is the dip angle of 183

the discontinuity or wedge, and no conversion is needed. The only caution to keep in mind 184

when calculating the F2 parameter is that it is always 1 for toppling failure. 185

Finally, the auxiliary angle C is the relation between discontinuity dip angle and slope 186

dip angle. Its calculation is also quite simple and is shown in Fig. 6 . For planar and wedge 187

failures C is equal to and , respectively, and can adopt positive (Fig. 6 - b) or 188

negative (Fig. 6 - a) values. For toppling, C is calculated as (Fig. 6 - c). Therefore, 189

the identification of the failure mode compatible with each discontinuity is required before the 190

calculation of this parameter. 191

192


10

Fig. 6 – Calculation of the auxiliary angle C. (a) and (b) show two possible cases of planar 193

failure; (c) shows a toppling. 194

Table 4 summarizes the formulas used for the calculation of A, B and C angular 195

relationships for the determination of F1, F2 and F3 parameters, respectively, using the dip and 196

dip direction of the slope and the discontinuities affecting the slope. 197

Table 4. Summary of the formulas used for the calculation of A, B and C angular 198

relationships. 199

Failure

mode Angular relationship Calculation of A Calculation of B Calculation of C

Planar |αj - αs| < 90º A = |αj - αs| B = j C = βj - βs

|αj - αs| > 90º A = 360º - |αj - αs| B = j C = βj - βs

Wedge |αi - αs| < 90º A = |αi - αs| B = i C = βi - βs

|αi - αs| > 90º A = 360º - |αi - αs| B = i C = βi - βs

Toppling 90º < |αj - αs| < 270º A=| |αj - αs| - 180º | Not necessary C = βj + βs

200

201

4. OPEN-SOURCE SOFTWARE DESCRIPTION 202

An open source software has been developed for an automatic and accurate calculation 203

of the angular relationships and parameters involved in the calculation of SMR 204

(https://personal.ua.es/en/ariquelme/smrtool.html). This software will help engineers and 205

geologists with a graphical representation of the geometry data used as input for the SMR 206

calculation and guiding them in the whole process. The process followed by the software for 207

the SMR assessment can be seen in Fig. 7. 208


11

209

Fig. 7 – Flowchart for the SMR calculation. 210

211

The pseudocodes of the processes A, F1, F2, C and F3 (Fig. 7) are described in the Algorithms 212

1 to 5 (Fig. 8 to 12). It is worth noting that when a wedge instability is being calculated, the 213

software equals αi = αj, and βi = βj using the same algorithm as for planar failure. 214

215

216

Fig. 8 – Algorithm 1. Pseudocode for the process A. 217

218

219


12

220

221

222

Fig. 9 - Algorithm 2 Pseudocode for the process F1. 223

224

225


227

228

Fig. 11 - Algorithm 4 Pseudocode for the process C. 229

230


13

231


233

A compact graphical user interface has been designed, allowing the user to check the 234

inputs and outputs in the same window. This graphical user interface is shown in Fig. 13 . The 235

Input data panel can be seen on the top left and the top centre of this figure. As input data, the 236

user must introduce the slope geometry (dip direction and dip), the slope excavation method, 237

which is chosen from a list, the discontinuity geometry (dip direction and dip) and the Rock 238

Mass Rating of the set of discontinuities for which the SMR wants to be calculated. In this 239

case, in which the analysis is being done for an individual set of discontinuities, the user must 240

choose the type of element analyzed between plane or wedge. If the user wants to run the 241

analysis not for one individual set of discontinuities but for all sets of discontinuities within 242

the rock mass, Planes and Wedges panel should be used. This panel is in the centre of the 243

upper half of the graphical user interface. Geometry and RMR for each discontinuity or set of 244

discontinuities to be considered have to be introduced here. In this case, it is not necessary to 245

select the type of element being analyzed, as after clicking the button “Calculate wedges”, the 246

software will calculate all the possible wedges from the intersecting plane discontinuities and 247

analyze if the failure is kinetically possible. When the wedge is kinetically non-possible a 248

value of 0 is shown in the possibility section of the Planes and Wedges panel, and the SMR 249

for this wedge is shown as equal to 100, meaning that there are no stability problems for this 250

wedge. 251


14

Based on the dip and dip direction of the slope and discontinuities (Clar’s notation), 252

the possible slope failure type is calculated by the software. As said in the previous section, 253

the formulae to be used to assess the parameters F1, F2 and F3 depends on the type of failure 254

considered (i.e. plane, wedge or toppling) and considers all possible geometrical situations 255

illustrated in Fig. 5 andFig. 6 . Therefore, the automatic assessment by the software avoids 256

mistakes in this step. 257

All the intermediate calculations are shown on the SMR Calculations panel. The upper 258

half of this panel shows the SMR auxiliary angles A, B, and C previously described. The 259

parameters F1, F2, F3 and F4 calculated according to Romana (1985) and Tomás et al. (2007) 260

are presented on the lower half panel, allowing users to compare the results obtained between 261

these two methods. 262

The SMR result is shown on the SMR Geomechanics Classification panel, which is in 263

the centre of the lower half of the graphical user interface. In addition to the SMR numerical 264

result, the stability classification of the slope, the description, the stability, the expected type 265

of failure and the remedial measurement recommended according to Romana (1993) are also 266

shown on this panel. Therefore, this is the results main panel, showing all the necessary data 267

to analyze the slope stability. 268

Finally, two graphical representations of the relative orientation between slope and 269

discontinuities are depicted at the right side of the interface, helping users to understand the 270

expected type of failure. The figure on the upper right-hand side shows a top view of the 271

angle between the slope and the discontinuity dip directions. Plane or wedge failure, but no 272

toppling, will be expected when the angle between these two vectors is less than 90º (acute 273

angle). On the contrary, only toppling can be expected when the angle is obtuse. The figure on 274

the lower right-hand side shows a cross section of the slope in which the discontinuity has 275

been depicted. This figure clarifies the type of failure expected (plane, wedge or toppling) 276

according to the slope and discontinuity geometry. These two figures have clarifying purpose 277

as they make clear the importance of related properties of the slope geometry and the 278

direction and dip of the discontinuities within the stability calculations, avoiding mistakes 279

involving the relative orientation between discontinuities and slope. It is worth noting that this 280

kind of miscalculation is the most common when applying SMR. 281

282


15

283

Fig. 13 – Graphical user interface of the SMRTool software. 284

285

5. CASE STUDY 286

A case study of an 18 m high slope composed of Jurassic slightly weathered limestone 287

(Martín and Campos 1974) with a strong structural control is presented in this section in order 288

to illustrate the applicability of the developed software and the calculation of the angular 289

relationships and correction parameters. A general view of the slope of the example is shown 290

in Fig. 14 . All the necessary geomechanical data obtained during the field works and in the 291

previous calculations for SMR assessment of the slope are summarized in Table 5. In this 292

case, three sets of discontinuities were recognized in the slope: DS1 to DS3. 293

294

Table 5. Data obtained in the field and previous calculations for SMR assessment. 295

Discontinuity set Dip Direction (º) Dip (º) RMRb

Slope

Mechanical excavation 209 79 --

DS1 189 62 60

DS2 92 90 62

DS3 346 54 62

296


16

297

Fig. 13 shows the SMRTool graphical user interface using the input data of Table 5. 298

These input parameters can be seen in the top centre panel in which dip direction and dip of 299

the slope are first shown. The dip direction and dip of the three sets of discontinuities are 300

included below. The mechanical excavation method is introduced in the top left panel, where 301

the data of plane 1 (discontinuity set 1) can also be seen. Once all the data have been 302

introduced, the SMR values for each discontinuity set is shown in the last column of the top 303

centre panel. SMR values of 36, 58 and 58 are obtained for DS1, DS2 and DS3, respectively. 304

The software runs the wedges analysis by clicking the Calculate wedges button in the top 305

centre panel. After doing this, the SMR values for the possible wedges are shown in the centre 306

of the graphical user interface. 307

308

309

Fig. 14 – View of the slope of the example where three discontinuity sets can be 310

distinguished. 311

312

In order to better understand the calculation process, the value of the auxiliary angles 313

A, B and C are shown in the SMR panel, where the likely failure mode is outlined. A, B and 314

C angles of 20º, 62º and -17º are obtained for plane 1 (DS1), being wedge or planar the 315

possible failure mode. The SMR factors are shown on the lower half of the SMR panel, where 316


17

it can be seen the difference between these factors calculated according to the discrete values 317

proposed by Romana (1993) and according to the continuous functions proposed by Tomás et 318

al. (2007). The first factor, for example, equals 0.4 when calculated by Romana (1993) and 319

0.5398 when calculated by Tomás et al. (2007). This example illustrates the benefit of using 320

the continuous functions for the factor assessment, especially when the parameters, are near 321

the borderline between two different ratings. In this case, the absolute value of the difference 322

between joint dip direction and slope dip direction for factor 1 equals 20º. Therefore F1 can be 323

rated as 0.4 or 0.7 according to Table 1 (Romana 1993), whilst the continuous functions do 324

not exhibit this issue. 325

The SMR numerical result for plane 1 (DS1) is shown in the SMR Geomechanics 326

Classification panel, being equal to 36 when the factors are calculated according to the 327

original discrete functions (Romana 1993) and equal to 29 when are calculated using the 328

continuous functions (Tomás et al. 2007). Despite the difference of the SMR value obtained 329

by these two methods for this example, for both cases, the stability classification is IV. Being 330

the description “bad” and unstable, with planar or big wedges failures expected, and important 331

corrective measures needed. Finally, the dip direction graphical representation shows the 332

alignment between slope and discontinuity dip direction, needed for factor 1 assessment. The 333

dip directions and failure mode representation let the user understand why a planar failure 334

mode is expected for plane 1 (DS1) (see the failure modes presented in Fig. 1 ). 335

We can change the data shown on the graphical user interface by clicking on the 336

number of the plane shown on the top left panel (i.e. the input data panel). If we set the plane 337

number 2 (DS2), all the data, results and plots shown will correspond to this plane, Fig. 15 . 338

In this case, toppling failure is expected, being all the calculations done (auxiliary angles, etc.) 339

according to this type of failure. Looking at the dip directions (upper right plot) and failure 340

mode representation (lower right plot) it can be seen that the slope and the discontinuity set 341

are dipping in opposite directions. Therefore, it is easy to understand why toppling is the 342

expected type of failure. The calculated SMR value for DS2 is equal to 58 and 57 calculated 343

by Romana (1993) and Tomás et al. (2007), respectively. Dip direction representation, where 344

no alignment between discontinuity and slope direction are seen, explains these SMR values 345

higher than those calculated for plane 1. For both SMR values (i.e. discrete and continuous), 346

the stability classification is III, described as “normal”, being partially stable with some joints 347

or many wedges expected, needing systematic corrective measures. It is noteworthy that the 348

results of the auxiliary angle A for DS2 are different when calculated according to the general 349


18

equation ||αj - αs| - 180º|, included in the detailed description of angular relationships of Table 350

4, and using the original equation |αj - αs - 180º| from Romana (1993). In this particular case, 351

the parallelism (A) is equal to 63º when it is calculated according to the proposed equation, 352

and this is the value shown by the SMRTool software, Fig. 15 and Table 6. However, a value 353

of 297º is obtained by the use of the original general equation published by Romana (1993). 354

By coincidence, the value of F1 is the same for both angles (0.15). Nevertheless, if the slope 355

dip direction were 60º smaller, F1 would be equal to 1 calculated with the proposed equation 356

and 0.15 calculated with the equation from Romana (1993). This miscalculation would lead to 357

a very different stability assessment. In fact, the calculation made using the relationships 358

listed in Table 5 would be on the safe of security in comparison with those made using the 359

general expression proposed by Romana (1993). 360

361

362

Fig. 15 – Graphical User Interface for plane 2. 363

364

The complete results of this case study are shown in Table 6. All the instabilities 365

possible combinations between slope and the three discontinuity sets are shown in this table. 366

One planar failure, two toppling and five wedges were analyzed by the software. The use of 367

the SMRTool allows the user to obtain all this data automatically, making more efficient and 368

quicker the calculation, and avoiding mistakes involving the relative orientation between 369


19

discontinuities and slope. For this case study, the discontinuity set 1 has the worst influence 370

on the stability of the slope. An SMR value of 36 has been obtained using the discrete 371

functions (Romana 1993) and of 29 using the continuous functions (Tomás et al. 2007). The 372

last wedge in Table 6 is not kinematically feasible, as the dip of the wedge is towards the 373

slope, therefore the software shows a value of 0 in the possibility button of the Planes and 374

Wedges panel, and the SMR for this wedge is shown as equal to 100. It means that there are 375

no stability problems for the considered wedge. 376

377

Table 6. Results obtained using SMRTool for the case study for discrete functions 378

when calculated by Romana (Romana 1993) and for continuous functions when calculated by 379

Tomás et al. (Tomás et al. 2007). 380

381

382

6. CONCLUSIONS 383

Slope Mass Rating (SMR) is worldwide used to perform a preliminary assessment of 384

rock slopes stability for different purposes such as civil or mining engineering. Nevertheless, 385

often some miscalculations are made when professionally and scientifically used. Nearly all 386

these mistakes involve the relative orientation between the slope and the discontinuities. 387

Therefore, a detailed description of the geometrical parameters A, B and C involved in the 388

calculation of SMR as never before done has been included in this paper. Furthermore, a 389

Matlab-based open-source software to avoid the above-mentioned mistakes as well as to make 390

more efficient and quicker the calculation of SMR has been programmed. The code of this 391

Matlab-based software is freely downloadable online for analysis of rock slope stability and 392

the algorithms are presented in this paper. 393

394

Type of

failure

Discontinuity

set involved

Auxiliary angles (º) SMR factors SMR value

A B C Discrete functions Continuous functions Discrete

functions

Continuous

functions F1 F2 F3 F4 F1 F2 F3 F4

Planar DS 1 20 62 -17 0.4 1 -60 0 0.5398 0.97157 -58.8778 0 36 29

Toppling DS 2 63 90 169 0.15 1 -25 0 0.17359 1 -25.6901 0 58 57

Toppling DS 3 43 54 133 0.15 1 -25 0 0.22623 1 -25.2288 0 58 56

Wedge DS 1 – DS2 27 61.82 -17.18 0.4 1 -60 0 0.37 0.97128 -58.8896 0 36 38

Wedge DS 1 – DS3 60.3 17.58 -61.42 0.15 0.15 -60 0 0.17803 0.23653 -59.6891 0 58 57

Wedge DS 2 – DS3 27 52.92 131.9 Non-feasible wedge 100 100


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7. ACKNOWLEDGEMENTS 395

This work has been supported by the University of Alicante under the projects 396

GRE14-04 and GRE17-11, and the Spanish Ministry of Economy and Competitiveness 397

(MINECO), the State Agency of Research (AEI) and the European Funds for Regional 398

Development (FEDER) under projects TEC2017-85244-C2-1-P and TIN2014-55413-C2-2-P, 399

and the Spanish Ministry of Education, Culture and Sport under project PRX17/00439 and 400

CAS17/00392. 401

402

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